Schubert Varieties and Linear Codes Associated to Schubert Varieties
Schubert Varieties , Schubert Code, Linear Codes
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In this book, we have explicitly discussed the codes associated with algebraic variety namely the Schubert variety which is a sub-variety of Grassmanians, and some properties of defined binary Schubert and extended binary Schubert code. The first chapter is introductory in nature. In this chapter, some basic facts and objectives of the book have been discussed. The second chapter consists of linear codes and its terminology which is being applied in the forthcoming chapter. In the third chapter, algebraic geometry and its linkage to coding theory have been discussed. The codes associated with ...
In this book, we have explicitly discussed the codes associated with algebraic variety namely the Schubert variety which is a sub-variety of Grassmanians, and some properties of defined binary Schubert and extended binary Schubert code. The first chapter is introductory in nature. In this chapter, some basic facts and objectives of the book have been discussed. The second chapter consists of linear codes and its terminology which is being applied in the forthcoming chapter. In the third chapter, algebraic geometry and its linkage to coding theory have been discussed. The codes associated with Schubert varieties have been discussed in the fourth chapter. A binary extended Schubert code of length 19 and Schubert Code of length 18 have been defined and some of its properties have been discussed. Chapter 6 discusses the implementation of Algebraic geometric Codes in the encoding and decoding process using MATLAB.
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